Oh, guys, also: every score in the Big Heart Machine store is 20% until Dec. 31st with the promo code "happyholidays": www.bigheartmachine.com/shop (When I was growing up, score were legit my favorite xmas gift, just saying...)

Percussionist here and as such I've spent a lot of time with Carter's solo pieces for timpani, which are also a great example of metric modulations. One thing I'd like to point out is part of the reason Carter used the term metric modulation was because he used them as structural markers of form since traditional tonal modulations were no longer really a part of music. (or at least not in a way which could be easily perceived by a listener) For that reason I think it still makes sense to call this device a "metric modulation" within the context of Carter's music, while in the broader context of music it probably would be better to call them tempo equations. So all metric modulations are tempo equations but not all tempo equations are metric modulations.

This was really great, thanks - I really need to explore Elliott Carter properly. This is a lovely way to cleanly notate this stuff...with the delivery to match, great stuff

Wow, this is awesome! thanks so much for making a video about this, I wasn't expecting that! Excellent content and happy holidays.

Yes, Modal equations. I'm all for it.

This is very, very educational.. thank you.

Brian thank you for the suggestion to listen to Elliott Carter’s first string quartet. The first metric modulation in the Carter is coincidentally the exact same I was trying to notate in my piece!!! Solved my problem instantly haha!

Procrastinating from writing a paper for an Elliott Carter class by watching this. I wish the piece I chose had more metric modulations...

That was a blast

A man who shares Sibelius hotkeys is a man after my heart

Thank you for a clear and well researched guide. In college in 2010 when I learned what a metric modulation is, we were taught the old 'Precedente' style of marking the new subdivision first followed by the old, without the Precedente version. It was a pop school where we did some jazz and it was okay, but not the sort of school (Tech Music Schools which is now BIMM) that would have you nurturing a culture of time changes really outside of musical theatre and nostalgic prog tunes because they made a lot of money. I agrere that we should adopt tempo equations into our usage, as one of the many ways that music notation should be able to adapt to more practical use.

Thanks for including the key commands; that might be the biggest headache of notation software. One example of metric modulation that I love happens in Jennifer Higdon's The Singing Rooms, between mvmts 1 and 2. The last measures of mvmt 1 have similar content, but the time signature decreases each measure while keeping the beat the same. So it goes from 4/4 to 3/4 to 2/4, giving the feeling of increased speed, then ending up in a much faster 4/4 than where it started. (I don't have the score right in front of me, but this is basically what happens.) Also, I've heard about the 103rd birthday concert. Is it true that they played a piece that Carter finished while sitting in the audience?

This was so helpful man! Thank you!! I've been trying to understand the metric modulation in 'Story' by Chon at 3:10 and how to put it on paper. Cheers!

You have such a delicate voice, it's so lovely.

I´m a jazz drummer and a matematician and I´m not sure that if the nomenclature "tempo equation" is appropriate. We should try to define matematically what is a "metric modulation". I guess that it is a bijective function f:R+ -------> R+ associated to the tempo change that comes from the metric modulation and it´s related with an algebraic equation with one unknown. An algebraic equation with one unknown is an expression of the form f(x)=0 where f(x) is a polynomial over the real field. So if I have a metric modulation (for example "quarter note=half note" ) this is equivalent to give an algebraic equation, the unknown "x" of this equation is the new tempo, so if I know the old tempo, the equation associated to the metric modulation allows me to calculate "x" i.e. the new tempo. At the same time this is equivalent to the existence of a bijective function f: R+ ------>R+ that for the old tempo of the piece ( a positive real number "t" ) gives me f(t) : the new tempo after the metric modulation. So your nomenclature "tempo equatión" makes sense but also we could say "tempo transformation" or "tempo bijection" or "tempo isomorfism" ( a bijective function is an isomorfism on the category "Set" of Sets and functions , this is a particular case of an area of matematics called "Category theory and functors" and I have done some research on that area). I should write this with rigor and develop some definitions and theorems and apply them to musical examples of metric modulations.

Great video! I'm orchestrating a thing, and the tempo modulates to triplet crotchets (one bar = 3 crotchet triplets). Is there a way to modulate this? Or is it more practicable to change the time signature from 4/4 to 2/4 and notate the bars with crotchet triplets. Many thanks if you're able to help :)

had no idea about click+opt when positioning objects, sooo helpful. i’d also love to hear your thoughts on microdivisions in notation-i.e music written 4/4 but every beat is subdivided into quintuplets, without using traditional triplet style

Young Walter White from an alternative universe hahahaha that’s a compliment 😁

I'm still trying to figure out what you mean when you say 'adding arrows like this' and then don't show the hotkey to do it. In my case, the metric modulation right click does not include the arrows, so I am using a separate text/right click to show arrows and then having to drop them over the metric modulation text.

What website do you use for the sheet music?

I have a question about the difference between the 2 (or 3) poly terms and I have already seen your previous video defining these terms (kzfaq.info/get/bejne/sK-EgpOct83FZo0.html) based on the definition of Henry Cowel. However I question the acceptance and validity of his definition against the definitions of metre and rhythms. I'm not assuming I'm correct just furthering the discourse, and questioning the blind acceptance of a past academic's take. By definition a simple 3:2 polyrhythm as you've described it (and is the accepted term for this) contains in the same duration of a measure, a 3/4 measure which is simple triple metre, over 2/2 , a simple duple metre. Hence 2 simultaneous metres, duple over triple. So by definition wouldn't that be polymeter? ... and with 5 vs 4 crotchet note grouping using accented rhythms to possibly imply different metre feel but measured at 4/4, wouldn't that technically still be polyrhythm under the same metric of simple quadruple metre with an implied metric difference by the rhythm but since its still measured against 4/4 it remains with a static metre and a polyrhythm..? And lastly in contradiction to keeping the concepts separate and some of my other points, doesn't having a 2 metres eg duple and triple, happening simultaneously, implied by 2 sets of rhythms mean they are in fact the same aural concept, which only has separation of meaning depending on the perspective when written i.e. 3:2 is 3/4 over 2/2 poly metre, but when written under 4/4 also 3 triplet crotchets over 2 minims (polyrhythm) and lastly back to polymeter 3/4 over 2/2 where the a crotchets would not have the same duration value so poly tempo? I also see the idea of 2 rhythms implying 2 metres (duple over triple) in the same metric, being defined as poly rhythm (different rhythms, same measure) but it's a sonic concept that holds relevance only in his it's written and which way the metric is applied, so 1 measure with 2 rhythms of the implied 2 metres of duple and triple (polymetre) taking up the same duration but the duration value of each crochet (rather than the semibreve) being different (polytempo) using a different time signature. Hence the confusion. Is it just an academic way of trying to quantify and label essentially the different perspective framing and measuremenf of the same sonic principle? Apologies in advance but this has been plaguing my thoughts since your last poly tempo vid (which was awesome). In context I'm a guy who questions the pronunciation of divīsive (devic-ive) based on the word divide when it would be less ambiguous in spoken language to pronounce it div-i-sive based on division. Also the use of past (rather than passed) to mean going beyond something e.g. having past the shop (outside a chronological context) - knowing the accepted grammar and understanding that "passed” in this use is not the past tense of the verb but still think that passed would work better as an exception and past be relegated to implying time.. .. so being that guy, I ask the above and question the accepted definitions of poly* when attached to , metre and rhythm ( more so than tempo). Thoughts are appreciated.

🤘🤘🤘🤘

I’ve recently written a song where one half is subdivided in quintuplets at 80 bpm and the other in sixteenths at 100 bpm, so the quintuplets and sixteenths are the same length. Kinda took a second to figure out how to notate it tho. I decided to use tuplets rather than a big denomination time sig. Makes for a really disorienting transition and I love the effect it makes.

Okay, but why have decided the time signature changed to 20/8?

How is this got only 2k

I call them "tempo modulations", because that's what they are.

not a single line of irrational time siggies ?